VAR模型應(yīng)用案例

VAR模型應(yīng)用實(shí)例眾所周知，經(jīng)濟(jì)的發(fā)展運(yùn)行離不開大量能源的消耗，尤其是在現(xiàn)代經(jīng)濟(jì)發(fā)展的過程中，能源的重要性日益提升。我國自改革開放以來，經(jīng)濟(jì)發(fā)展取得長(zhǎng)足的進(jìn)步，經(jīng)濟(jì)增長(zhǎng)率一直處于較高的速度，經(jīng)濟(jì)的高速增長(zhǎng)帶來了能源的大量消耗，進(jìn)而帶來了我國能源生產(chǎn)的巨大提高。因此，研究經(jīng)濟(jì)增長(zhǎng)率與能源生產(chǎn)增長(zhǎng)率之間的關(guān)系具有重要的意義，能為生源生產(chǎn)提供一定的指導(dǎo)意義。1.基本的數(shù)據(jù)我們截取1978-2015年中國經(jīng)濟(jì)增長(zhǎng)速度（GDP增速）和中國能源生產(chǎn)增長(zhǎng)速度數(shù)據(jù)，具體數(shù)據(jù)如下：表11978——2016年中國經(jīng)濟(jì)和能源生產(chǎn)增長(zhǎng)率年份國內(nèi)生產(chǎn)總值增長(zhǎng)速度（%）能源生產(chǎn)增長(zhǎng)速度（%）年份國內(nèi)生產(chǎn)總值增長(zhǎng)速度（%）能源生產(chǎn)增長(zhǎng)速度（%）197811.710.419979.20.319797.63.719987.8-2.719807.8-1.319997.71.619815.1-0.820008.55198295.620018.36.4198310.86.720029.16198415.29.220031014.1198513.49.9200410.115.619868.93200511.411.1198711.73.6200612.76.9198811.25200714.27.919894.26.120089.7519903.92.220099.43.1

19919.30.9201010.69.1199214.22.320119.59199313.93.620127.93.21994136.920137.82.21995118.720147.30.919969.93.120156.91.22.序列平穩(wěn)性檢驗(yàn)（單位根檢驗(yàn)）使用Eviews9.0來創(chuàng)建一個(gè)無約束的VAR模型，用gdp表示的是中國經(jīng)濟(jì)的增長(zhǎng)率，用nysc表示中國能源生產(chǎn)的增長(zhǎng)率，下面分別對(duì)gdp和nysc進(jìn)行單位根檢驗(yàn)，驗(yàn)證序列是否平穩(wěn)，能否達(dá)到建立VAR模型的建模前提。KdSeries:GDPWorkfile:UNTITLED::Untitled\ |1=1||回ViewProcObjectPropertiesPrintNameFreezeSampleGenrSheetGraphAugment&dDick&y-FullerUnitRootTestonGDPNullHypothesis:GDPhasaunitrootExogenous:ConstantLagLength:3[Automatic-basedonSIC,maxlag=9)t-Statistic Prob*AugmentedDickey-Fullerteststatistic -3.867553 0.0056Testcriticalvalues: 1%level -3.6394075%level -2.95112510%level -2.614300*MacKinnon(1996)one-sidedp-valuesAugmentedDickey-FullerTestEquation□ependentVariable:D(GDP)Method:LeastSquaresDate:05^17/17Time:10:55Sample(adjusted):19322015Includedobservations:34afteradjustmentsVariableCoefficientStd.Errort-StatisticProb.GDP(-1)-0.8551710.2211U-3.S675530.0006D(GDP(-1D0.6256310.1935293.2227550.0031D(GDP(-2)}0.0492400.1755170.2S0&440.7811D(GDP(-3))0.2649370.1673481.5831450.1242C3.5400502.2229613.0417450.0006R-squared0.-458475Meandependentvar0.052941AdjustedR-squared0.3S37S2S.D.dependentvar2.5457311 fiKrridnnmiTT-jflTETCNM圖2.1經(jīng)濟(jì)增速（GDP）的單位根檢驗(yàn)

圖2.2能源生產(chǎn)增速（nysc）的單位根檢驗(yàn)符合建模的經(jīng)過檢驗(yàn)，在1%的顯著性水平上，gdp和nysc兩個(gè)時(shí)間序列都是平穩(wěn)的，條件，我們建立一個(gè)無約束的VAR模型。符合建模的3.VAR模型的估計(jì)

ViewProcObjectPrintNameFreezeEstimateForecastSVectorAutor&gressionEstimatesVectorAutoregressionEstimates□ate:05/17/17Time:11:03Sample(adjusted):19002015Includedobservations:36afteradjustmentsStandarderrorsin(J&t-statisticsin[]GDPNYSCGDP(-1)0.0255440.271598(0.16499)(0.23599)[5.00369][1.-15086]GDP[-2)-0.5304-95-0.292356(0.16625)(0.23730)[-3.19096][-1.22942]NYSC(-1}-0.0522250.046356(0.11565)(0.-16543)[-0.45156][5.11612]NYSC(-2)0.-186100-0357568(0.11349)(0.-16234}[1.63977][-2.20263]C6.-1945182.363291ft50887)(2.-15827}[410539][132666]R-squared0.4925650.554387Adj.R-squared0.4270S90.4-96SS9Sumsq.resids130.5151267.0333S.E.equation2.0513692.934958F-statistic7.5223909.641791Loglikelihood-74.26525-37.15117AkaikeAIC44036255.119509SchwarzSC4.6235535.3394-42Meandependent9.7383395.016667S.D.dependent2.7103544-.137S05Determinantresidcovariance(dotadj.)30.72390Determinantresidcovariance22.78215Loglikelihood-1584312Akaikeinformationcriterion9.357287Schwarzcriterion9.797154圖3.1模型的估計(jì)結(jié)果?Var:VAR01Workfile:完成的VAR模型::Untitled、 |d||回||K^ViewPracObjectPrintWameFreeze!EstimateForecastStats|lmpuL5e|ResLd5|^stimation.Proc：LS12GDFNYSCgModel：GDF=C（L1）*GDF（-1）+C（L2）*GDF（-2）+C（L3）*NYSCH）+C（L4）*1TYSC（-2）+C（L5）NYSC=C（2?1）*GDF（-1）+C（2,2）*GDF（-2）+C（2?3）*NYSC（-1）+C（2,4）*NYSC（-2）+c（mVAB.Model一SubstitutedCoe￡￡icients:GDF=0.825544312835*GDF（-1）-0.530494707484*GDP（-2）-0.0522247695102*NYSC（-1）+0.186100460724*NYSC（-2）+6.19451824花3NYSC=0.271597998674*GEP（-1）-0.292356168154*GDF（-2）+0.846355866747*NYSC（-1）-0.357567632748*NYSC（-2）+2.86329108178圖3.2模型的表達(dá)式4.模型的檢驗(yàn)4.1模型的平穩(wěn)性檢驗(yàn)回VanUNTITLEDWorHile:UNTITLED::Untiltled\ViewProcObje吐PrintNameFreezeEstimateForecastVARStabilityConditionCheckRootsofCharacteristicPolynomialEndogenousvariables:GDPNYSCExogenousvariables:CLagspecification:12DaiK05/17/17Time:11:11RootModulus0.566086-0.45170810.7242200.566086+0.45170810.7242200.269364-0.62655110.6321960.269364+0.62655110.632196Norootliesoutsidetheunitcircle.VARsatisfiesthestabilitycondition.圖4.1.1AR根的表由圖4.1.1知，AR所有單位根的模都是小于1的，因此估計(jì)的模型滿足穩(wěn)定性的條件。通過對(duì)GDP增長(zhǎng)率和能源生產(chǎn)增長(zhǎng)率進(jìn)進(jìn)行了VAR模型估計(jì)，并采用AR根估計(jì)的方法對(duì)VAR模型估計(jì)的結(jié)果進(jìn)行平穩(wěn)性檢驗(yàn)。AR根估計(jì)是基于這樣一種原理的:如果VAR模型所有根模的倒數(shù)都小于1，即都在單位圓內(nèi)，則該模型是穩(wěn)定的;如果VAR模型所有根模的倒數(shù)都大于1，即都在單位圓外，則該模型是不穩(wěn)定的。由圖4.1.2可知，沒有根是在單位圓之外的，估計(jì)的VAR模型滿足穩(wěn)定性的條件。4.2Granger因果檢驗(yàn)網(wǎng)Var:VARO1Workfile:完成的VAR模型::Untitled、ViewProcObjectPrintName!Freeze[EstimateForecastStatsImpulVARGrangerCausality/BlockExogeneityWaldTestsDate:05^19^17Time:20:57Sample:19782015Included!observations:36Dependentvariable:GDPExcludedChi-sqdfProb.NYSC303869820.21S9All3.03869820.2189Dependentvariable:NYSCExcludedChi-sqdfProb.GDP1.893231圖4.2.1[Granger因果檢驗(yàn)結(jié)果圖All1.89320120.3871Granger因果檢驗(yàn)的原假設(shè)是：H0：變量x不能Granger引起變量y備擇假設(shè)是：H1：變量x能Granger引起變量y對(duì)VAR（2）進(jìn)行Granger因果檢驗(yàn)在1%的顯著性水平之下，經(jīng)濟(jì)增速（GDP）能夠Granger引起能源生產(chǎn)增速（NYSC）的變化，即拒絕了原假設(shè)；同時(shí)，能源生產(chǎn)增速（NYSC）能夠Granger經(jīng)濟(jì)增速（GDP）的變化，即拒絕了原假設(shè)，接受備擇假設(shè)。5滯后期長(zhǎng)度回VanUNTITLEDWorlcfile:UNTITLED::Untitled、ViewProcObjectPrintNameFreezeEstimateForecastStatsImpulseResidsZoomVARLagOrderSelectionCriteriaEndogenousvariables:GDPNYSCExogenousvariables:C□ate:05^17/17Time:11:16Sample:19732015Includedobservations:34LagLogLLRFPEAICSCHQ0-172.7423NA99.3069610.2789610.36374-10.309581-158.355025.32394-55.341499.6973519.9667099.7392102-143.079718.38127indicateslagorderselectedindicateslagorderselectedbythecriterionLR:sequentialmodifiedLRteststatistic(eachtestat5%level)FPE:FinalpredictionerrorAIC:AkaikeinformationcriterionSC:SchwarzinformationcriterionHQ:Hannan-Quinninformationcriterion圖5.1VAR模型滯后期選擇結(jié)果從上圖可以看出LR,FPE,AIC,SC,HQ都指向同樣的2階滯后期，因此應(yīng)該選擇VAR(2)進(jìn)行后續(xù)的分析。37.61303*9.298803*9.747733*9.451906*3-14749830.92353446.343659.4-9939710.123409.7142344--14549842.94-091652.358339.61755510.425639.893131

6.脈沖函數(shù)況；而能源生產(chǎn)（6.脈沖函數(shù)況；而能源生產(chǎn)（NYSC）的變化是在第九期的時(shí)候?qū)崿F(xiàn)持平的狀態(tài)。11111 11111 11111 11111 11111 111毋 in 哼 2D b心KTEUciNYSC始宣將能源生產(chǎn)增長(zhǎng)率（NYSC）對(duì)于經(jīng)濟(jì)增長(zhǎng)率（GDP）的脈沖響應(yīng)分析，當(dāng)給經(jīng)濟(jì)增長(zhǎng)一個(gè)正的沖擊的時(shí)候，在前兩期是呈現(xiàn)一個(gè)下降的趨勢(shì)，主要的原因應(yīng)該是，經(jīng)濟(jì)增長(zhǎng)促進(jìn)能源生產(chǎn)的提高是存在滯后期的，但是但很快就出現(xiàn)了上升的趨勢(shì)在第五期的時(shí)候達(dá)到最大值，之后出現(xiàn)了下降的趨勢(shì)，然后又回升，直到第十期之后保持了平衡。這說明經(jīng)濟(jì)增長(zhǎng)對(duì)于能源生產(chǎn)增長(zhǎng)的影響是正向的，會(huì)呈現(xiàn)一種上升、下降、平衡的基本狀態(tài)，說明經(jīng)濟(jì)發(fā)展對(duì)能源生產(chǎn)的促進(jìn)作用并不是無限的，經(jīng)過一定作用之后看，會(huì)出現(xiàn)一種平衡狀態(tài)。經(jīng)濟(jì)增長(zhǎng)率（GDP）對(duì)于能源生產(chǎn)增長(zhǎng)率（NYSC）的脈沖響應(yīng)分析，經(jīng)過對(duì)比圖中第2幅和第3幅小圖，我們大致是可以看出兩者之間是呈現(xiàn)完全相反的情況。當(dāng)在本期給能源生產(chǎn)增長(zhǎng)率（NYSC）一個(gè)正沖擊之后，前兩期是增長(zhǎng)，然后到第五期是下降趨勢(shì)，然后回升，在第七期之后基本上持平。

7.方差分析回VanUNTITLEDWorkfle:UNTITLED::Untitled\ |■=■回1ViewProcObjectPrintNameFreezeEstimateForecastStatsImpulseResidsZoomVarianceDecompositionVarianceDecompositionofGDP:PeriodS.E.GDPNYSC12.051869100.00000.00000022.62673299.711540.23845032.6695589&721431.2785704-2.76860692.91947706053352.34515339.1101110.8893962.351171S88S71311.1123772.35882733.4300711.5699332.37241037.63734123626692.37677737.4-049012.59510102.37602037.4-023112.59769112.377548873871112.61239122.37S29637.3730712.62693132.3704-8137.3670712.63293U2.373525373650912.63491152.373573373650812.63492162.378601373652412.63476172.37861337364-6612.63534182.378625373639212.63603192.37862937.3636812.63632202.37863037.3636912.63631212.373631873636412.63636222.373632373635812.63642232.37863337363561263644242.37863337363561263644252.37863337363561263644262.37863337363561263644272.37863337.363561263644282.37363337.363561263644292.37363337363561263644302.37363337363561263644圖7.1經(jīng)濟(jì)增長(zhǎng)（GDP）方差分析結(jié)果

@Var:UNTITLEDWorkfi1e:UNTITLED::Untitled\□回ViewProcObjectPrintNameFreezeEstimateForecastStatsImpulseResidsZoomVarianceDecompositionVarianceDecompositionofNYSC:APeriodSE.扣PNYSC12.934953152824234.7175324.02209122.5767677.4232434.19194323.7934076.206524-4.20362924.1765175.3234954.26613426.2479573.7520564.29387527.1457072.3543074.30702327.0992872.90072043147B027.06764-72.93236g431840127.1067672.3932410431&99627.1252272.374-7311432022527.1145572.38545124.32125427.1025772.3974313432146327.09994-72.9000614432140727.1006972.3993115432158327.1015972.39